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Assessment
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Illustrative Mathematics

Operations with Rational and Irrational Numbers

For Teachers 9th - 12th Standards
Learners complete addition and multiplication tables that include rational and irrational numbers. They also answer a series of questions about the sums and products of irrational and rational numbers. One suggested modification would be...
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Lesson Plan
Curated OER

Algebra 1: Simplifying Radicals

For Teachers 8th - 9th Standards
After discussing the difference between rational and irrational numbers, the class pratices simplifying, adding, and subtracting radical expressions. They play a game which involves passing around cards until they have matching hands of...
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Lesson Plan
Curated OER

Add Positive And Negative Numbers

For Teachers 6th - 8th
Scholars investigate the concept of adding positive and negative numbers. They practice adding using the number line for scaffolding. This can be done as a game for younger learners, but may also be helpful for engaging the older pupils.
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Worksheet
Curated OER

Rational or Irrational

For Students 7th
In this rational and irrational numbers worksheet, 7th graders solve 24 different problems that include defining various rational and irrational numbers and/or expressions. First, they identify whether each given number and/or expression...
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Worksheet
Curated OER

Quadratics with Irrational Solutions

For Students 8th - 11th
In this algebra worksheet, students apply the concepts of a right triangle to help them solve for the missing sides of a triangle. They use the quadratic formula to solve word problems. There are 5 problems with an answer key.
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Lesson Plan
Virginia Department of Education

Ground Zero

For Teachers 6th
Don't harbor any negative feelings toward negative numbers. Scholars learn about different classifications of rational numbers, including negative integers. They also develop definitions of the opposite and the absolute value of a...
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Lesson Plan
Curated OER

Worksheet One - Definite Integral

For Teachers Higher Ed
In this definite integral worksheet, students use substitution to simplify integrals. They find the values of the upper and lower points and interpret points found on a graph. Students solve this two-page worksheet.
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Worksheet
Curated OER

Irrational Numbers

For Students 9th
In this irrational numbers worksheet, 9th graders solve 10 different problems that include determining the approximations of various irrational numbers. First, they solve each irrational number in the first set to the nearest tenth....
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PPT
Curated OER

Calculator Tricks: The Golden Prediction

For Teachers 6th
Excite the class with a mathematical trick, a calculator, and a good number sense. They use the directions provided on each slide to make a list of numbers, use their calculator to divide, and find the golden mean. A little history on...
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Lesson Plan
Curated OER

Number Types: Where Vocabulary Meets Numbers

For Teachers 6th - 12th Standards
Rational, irrational, real, natural. All these words can refer to numbers. Who knew? Learners use the Visual Thesaurus and a semantic feature analysis grid to examine the different attributes of numbers. Step-by-step instructions for...
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Unit Plan
Benjamin Franklin High School

Saxon Math: Algebra 2 (Section 1)

For Teachers 9th - 12th Standards
This first of twelve algebra 2 resources provides a broad review of many algebra 1 concepts through a number of separable lessons and labs. Starting with the real number system and its subsystems, the sections quickly but thoroughly move...
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Lesson Plan
EngageNY

The Long Division Algorithm

For Students 8th Standards
Two methods are always better than one! The eighth installment in this series asks pupils to convert decimals to fractions using two approaches. Individuals first use the more traditional approach of long division and then use reverse...
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Lesson Plan
Curated OER

Babylonian Mathematics I

For Teachers 8th - 10th
Learners examine a Babylonian clay tablet and the mathematics found on it as a catalyst to investigate a variety of mathematical ideas. They work with prime numbers, classify numbers as whole, integer, rational, or irrational and use...
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Lesson Plan
EngageNY

Inverses of Logarithmic and Exponential Functions

For Teachers 11th - 12th Standards
Revisit the relationship between logarithms and exponentials. Learners review the notion of logarithms as the way to solve exponential equations in the 21st segment in a Pre-calculus series of 23. Pupils use the knowledge to prove that...
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Worksheet
Kuta Software

Sets of Real Numbers

For Students 7th - 9th Standards
Real and unreal, rational and irrational, your learners will become experts at labeling numbers with this worksheet. A full sheet of different numbers requires your mathematicians to label each number with any category that fits that...
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Lesson Plan
Curated OER

Number Theory - Week 12

For Teachers 12th - Higher Ed
For this number theory worksheet, students study integers and their properties. They explore the Fibonacci Sequence and approximate irrational numbers. This two-page worksheet contains eight problems.
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Lesson Plan
Curated OER

Numbers Beyond Reason!

For Teachers 4th
Fourth graders use the story of the discovery of irrational numbers to explore the different classes of numbers, the different ways in which numbers may be represented, and how to classify different numbers into their particular class.
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Worksheet
Curated OER

Signed Numbers

For Students 6th
In this signed numbers worksheet, 6th graders solve and complete 4 different types of problems. First, they calculate each problem using a number line. Then, students solve each word problem as indicated.
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Lesson Plan
Curated OER

Real Number System Graduated Bowl Activity

For Teachers 8th
Eighth graders determine which numbers are rational numbers. For this number lesson students answer a series of questions related to natural and whole numbers as well as integers and rational numbers. Students work cooperatively in groups.
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Assessment
Inside Mathematics

Rugs

For Teachers 8th Standards
The class braids irrational numbers, Pythagoras, and perimeter together. The mini-assessment requires scholars to use irrational numbers and the Pythagorean Theorem to find perimeters of rugs. The rugs are rectangular, triangular,...
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Handout
Charleston School District

Estimating Values of Expressions

For Students 8th Standards
You can't evaluate an irrational root expression without a calculator—or can you? Scholars estimate the value of roots within an expression to approximate the value of the expression. Expressions include a mix of square roots and whole...
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Assessment
Charleston School District

Review Unit 7: Real Numbers

For Students 8th Standards
Provide pupils with problems to check their understanding of the concepts within the unit. The seven-part series of lessons covers concepts related to irrational numbers. Learners convert between fractions and decimals, estimate the...
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Assessment
Charleston School District

Pre-Test Unit 7: Real Numbers

For Students 8th - 9th Standards
Don't be irrational! Use this pre-test to assess your classes' ability to work with all types of real numbers. The lesson asks learners to estimate value, evaluate roots, and order numbers. This begins a series of lessons on the real...
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Lesson Plan
EngageNY

What Is Area?

For Teachers 9th - 10th Standards
What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and upper...

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